Question

Innovation Company is thinking about marketing a new software product. Upfront costs to market and develop the product are $5.00

million. The product is expected to generate profits of $1.00

million per year for ten years. The company will have to provide product support expected to cost $100,000

per year in perpetuity. Assume all profits and expenses occur at the end of the year.

a. What is the NPV of this investment if the cost of capital is 6.0%

Should the firm undertake the? project? Repeat the analysis for discount rates of 2.0%

and 11.0%?, respectively.

b. What is the IRR of this investment? opportunity???

c. What does the IRR rule indicate about this? investment?

Answer 1

Answer to Question a,

NPV = present value of cash inflow -PV of Cash outflow.

present value of cash inflow? = PV Annuity factor X annual cash flow.

PV Annuity factor ? = (((1+i)ⁿ)-1) / (((1+i)ⁿ)(i)),

n = 10 years, i is the interest rate = 6% or 0.06,

=((1.06¹⁰)-1) / ((1.06¹⁰)(0.06)),

= 7.3600870514147,

present value of cash inflow? = 7.3600870514147 X 1,000,000 = $7,360,087.0514147

To find present value of product support expected cost of $100,000, is devided by the cost of capital of 6%.

Present value of product support expected cost = $100,000 / 6% = $1,666,666.66666667,

PV of Cash outflow= Initial outlay + Perpetuity amount of annual product support cost,

= $5,000,000 + $1,666,666.66666667 = $6,666,666.66666667,

NPV = $7,360,087.0514147 - $6,666,666.66666667 = $693,420.38474803. Since NPV is positive, The firm will undertake the project

Repeated at discount rates of 2.0%,

NPV = present value of cash inflow -PV of Cash outflow.

present value of cash inflow? = PV Annuity factor X annual cash flow.

PV Annuity factor ? = (((1+i)ⁿ)-1) / (((1+i)ⁿ)(i)),

n = 10 years, i is the interest rate = 2% or 0.02,

=((1.02¹⁰)-1) / ((1.02¹⁰)(0.02)),

= 8.98258500624224,

present value of cash inflow? = 8.98258500624224 X 1,000,000 = $8,982,585.00624224,

To find present value of product support expected cost of $100,000, is devided by the cost of capital of 2%.

Present value of product support expected cost = $100,000 / 2% = $5,000,000

PV of Cash outflow= Initial outlay + Perpetuity amount of annual product support cost,

= $5,000,000 + $$5,000,000 = $10,000,000

NPV = $8,982,585.00624224 - $10,000,000 = $-1,017,414.99375776,

Since NPV is negative, The firm will not undertake the project.

Repeated at discount rates of 11.0%,

NPV = present value of cash inflow -PV of Cash outflow.

present value of cash inflow? = PV Annuity factor X annual cash flow.

PV Annuity factor ? = (((1+i)ⁿ)-1) / (((1+i)ⁿ)(i)),

n = 10 years, i is the interest rate = 11% or 0.11,

=((1.11¹⁰)-1) / ((1.11¹⁰)(0.11)),

= 5.88923201114121,

present value of cash inflow? = 5.88923201114121 X 1,000,000 = $5,889,232.01114121,

To find present value of product support expected cost of $100,000, is devided by the cost of capital of 11%.

Present value of product support expected cost = $100,000 / 11% = $909,090.909090909

PV of Cash outflow= Initial outlay + Perpetuity amount of annual product support cost,

= $5,000,000 + $909,090.909090909 = $5,909,090.90909091

NPV = $5,889,232.01114121 - $5,909,090.90909091 = $-19,858.8979497002

Since NPV is negative, The firm will not undertake the project.

Answer to Question b,

Inorder to find the IRR, We have to arrive 2 discount rates on which one discount rate provides Positive NPV is termed as lowest discount rate, and another provides Negative NPV which will be termed as Highest rate. Here these rates are found out in answer for Question (a) above.

Lowest rate = 6%, Highest rate = 11%,

IRR formula will be = Lowest Rate + (NPV at Lowest rate / (NPV at Lowest rate - NPV at highest rate)) (Hoghest rate - Lowest rate ),

NPV at Lowest rate = $693,420.38474803,

NPV at Highest rate = $-19,858.8979497002, applying values in formula,

= 6% + (($693,420.38474803 / ($693,420.38474803 - $-19,858.8979497002) (11 - 6 ))%,

= 6% + 4.86079156908504 % = 10.860791569085%, rounded to 2 decimal places = 10.86%.

Answer to Question c,

This IRR denotes the return from the project. and its cost of capital is 6%, According to IRR rule a project is said to be accepted only if it's Cost of capital is less than the project IRR. Here the IRR is  10.86%. and cost of capital only 6%, so the project should be Accepted.

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